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Lumifer comments on Probabilities Small Enough To Ignore: An attack on Pascal's Mugging - Less Wrong
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About as unfathomably small as the number of 3^^^3 people is unfathomably large?
I think you're relying on "but I feel this can't be right!" a bit too much.
I don't see what your point is. Yes that's a small number. It's not a feeling, that's just math. If you are assigning things 1/3^^^3 probability, you are basically saying they are impossible and no amount of evidence could convince you otherwise.
You can do that and be perfectly consistent. If that's your point I don't disagree. You can't argue about priors. We can only agree to disagree, if those are your true priors.
Just remember that reality could always say "WRONG!" and punish you for assigning 0 probability to something. If you don't want to be wrong, don't assign 1/3^^^3 probability to things you aren't 99.9999...% sure absolutely can't happen.